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L08_a - STANDING WAVES(14.3 in text First reminder about...

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STANDING WAVES (14.3 in text) First: reminder about DIRECTION OF PROPAGATION : determined by signs of x and t terms in phase o ( ) t kx A y ω = sin 1 goes in + x direction o ( ) t kx A y ω + = sin 2 goes in - x direction Why? o To keep phase ( ) t kx ω at fixed value (i.e. particular feature on wave) as t increases, x must also increase. [opposite for ( ) t kx ω + ]

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STANDING WAVES: Look at 2 waves going in opposite directions in same medium o ( ) t kx A y ω = sin 1 o ( ) t kx A y ω + = sin 2 Superposition Resultant wave o o Not a traveling wave Standing wave ( ) ( ) [ ] t x k A t x k t x k t x k t x k A t kx A t kx A y y y ω ω ω ω ω ω ω cos sin 2 sin cos cos sin sin cos cos sin sin sin 2 1 R = + + = + + = + =
Resultant t x k A y ω cos sin 2 R = is a STANDING WAVE Each part of string oscillates with SHM and amplitude x k A sin 2 o Means amplitude depends on position x Where 1 sin ± = kx , amplitude is a maximum ANTINODE o Antinodes for Since λ π 2 = k means ANTINODES are at L , 4 5 , 4 3 , 4 λ λ λ = x o i.e. at odd multiples of

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